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Title Implementation and evaluation of a splitting method for Total Variation deblurring
Author Lassen, Allan Lyngby
Supervisor Hansen, Per Christian (Scientific Computing, Institut for Informatik og Matematisk Modellering, Danmarks Tekniske Universitet, DTU, DK-2800 Kgs. Lyngby, Denmark)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2011
Abstract This thesis takes basis in the solution to the inverse problem; the image deblurring problem, and more specifically the Total Variation (TV) solution hereof. In the field of research that is occupied with image deblurring, it is a well known fact that this type of solution generally gives very visually pleasing results, but at the cost of more complex computations. Some of the relevant theory behind Inverse Problems will be covered, such as the Fredholm integral equation, and an explanation of how this connects to the model for image deblurring. Some introductory topics that leads to some of the simpler methods that solve this problem, e.g. the 2-norm Tikhonov solution and fast algorithms to decompose structured matrices will be also covered in the introductory sections. Total Variation and the computational issues that follows with the use of this type of solution is described along with some of the actual implementations of how these problems are treated through different algorithms. Part of the thesis will be focused on the theory of the relatively new type of solvers of the TV deblurring problem, the so-called splitting method. One specific method will be chosen for implementation, and the code for this method will accordingly be implemented in Matlab and tested to see its computational properties. A number of Matlab methods, for which code is publicly available, will similarly be analyzed in terms of their algorithmic specifications, and will be applied to a set of chosen test problems as well as tested for their performance and usability for the average user. Finally, the effect of the regularization parameters will be analyzed with respect to noise, blur and image type.
Imprint Technical University of Denmark (DTU) : Kgs. Lyngby, Denmark
Series IMM-M.Sc.-2011-12
Original PDF ep11_12.pdf (29.66 MB)
Admin Creation date: 2011-03-24    Update date: 2011-03-24    Source: dtu    ID: 275691    Original MXD